Close-in tones

ABSTRACT

A system can include a close-in tone control configured to detect a set of close-in tones of an interleaved analog to digital converter (IADC) signal and output a trigger signal in response to the detection. The system can also include a close-in tone mismatch estimator configured to determine a correlation and a power estimate for the set of close-in tones in the IADC signal in response to the trigger signal.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority to the Indian (IN)Patent Application entitled: “NOVEL TIME DOMAIN CORRECTOR IN THEPRESENCE OF INTERFERENCE IN AN INTERLEAVED ADC”, Application No.:1310/CHE/2014, filed on 12 Mar. 2014, which is incorporated herein byreference. Additionally, this application is related to the followingcommonly assigned co-pending U.S. patent applications entitled:“MISMATCH PROFILE”, Ser. No. 14/656,205 and “MISMATCH CORRECTOR”, Ser.No. 14/656,122; all of which are filed contemporaneously herewith andare incorporated herein by reference.

TECHNICAL FIELD

This disclosure relates to systems and methods for detecting close-intones. More particularly, this disclosure relates to systems and methodsfor detecting close-in tones of an interleaved analog-to-digitalconverter signal. Additionally or alternatively, this disclosure relatesto preventing an impact of interferers on mismatch profile estimation.

BACKGROUND

An analog-to-digital converter (ADC, A/D, or A to D) is a device thatconverts a continuous physical quantity (e.g., voltage) into a digitalnumber that represents the quantity's amplitude. The analog-to-digitalconversion involves quantization of the input, such that a small amountof error is introduced. Moreover, instead of doing a single conversion,an ADC often performs the conversions (“samples” the input)periodically. The result is a sequence of digital values that have beenconverted from a continuous-time and continuous-amplitude analog signalto a discrete-time and discrete-amplitude digital signal.

A time-interleaved ADC uses N parallel ADCs where each ADC samples dataevery Nth cycle of the effective sample clock, where N is a positiveinteger greater than one. The result is that the sample rate isincreased N times compared to what each individual ADC can manage.

SUMMARY

Systems and methods for detecting close-in tones. Additionally oralternatively, systems and methods are described for preventing animpact of interferers on mismatch profile estimation.

One example relates to a system that can include a close-in tone controlconfigured to detect a set of close-in tones of an interleaved analog todigital converter (IADC) signal and output a trigger signal in responseto the detection. The system can also include a close-in tone mismatchestimator configured to determine a correlation and a power estimate forthe set of close-in tones in the IADC signal in response to the triggersignal.

Another example relates to an integrated circuit (IC) chip. The IC chipcan include an analog-to-digital converter (ADC) interleaver includes aplurality of ADCs that are each configured to sample an analog signal inresponse to a clock pulse. The interleaved ADC outputs an IADC signalthat includes a plurality of spurs formed from mismatches between theplurality of ADCs. The IC chip can also include a frequency domainprocessor that determines a frequency domain representation of theinterleaved IADC signal. The IC chip can further include a close-in tonecontrol configured to detect a set of close-in tones of the IADC signalbased on the frequency domain representation of the IADC signal. Theclose-in tone control can also be configured to receive data from amismatch profile estimator characterizing an estimate of a mismatchprofile for a tone near in frequency the set of close-in tones. Theclose-in tone control can still further be configured to output atrigger signal in response to detecting that an Fast Fourier Transform(FFT) bin corresponding to the set of close-in tones has a power above apower threshold and in response to determining that the estimate of themismatch profile for the tones near in frequency the set of close-intones has an uncertainty above an uncertainty threshold. The IC chip canfurther include a close-in tone mismatch estimator determines acorrelation and a power estimate for the set of close-in tones in theIADC signal in response to the trigger signal.

Yet another example relates to a method that includes randomizingselection of blocks of samples an interleaved analog-to-digital (IADC)signal to provide randomly selected blocks. The method also includesapplying a windowing function to the randomly selected blocks of samplesof the IADC signal. The method further includes applying an FFT to theselected blocks of samples to determine a frequency domainrepresentation of the IADC signal. The method yet further includesestimating a frequency domain mismatch for the interleaved ADC signal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example of a system for determining a mismatchprofile of an interleaved analog-to-digital converter (ADC).

FIG. 2 illustrates another example of a system for determining amismatch profile of an interleaved ADC.

FIG. 3 illustrates an example of a graph depicting an output of aninterleaved ADC without mismatch correction.

FIG. 4 illustrates an example of a diagram that depicts the amplitude oftones and images of tones as a function of Fast Fourier Transform (FFT)bin index.

FIG. 5 illustrates a conceptual example of a randomized block selection.

FIG. 6 illustrates a block diagram of an example of a random numbergenerator.

FIG. 7 illustrates a graph that illustrates close-in tones.

FIG. 8 illustrates a block diagram of a trigger control.

FIG. 9 illustrates a block diagram of a close-in tone mismatchestimator.

FIGS. 10-13 depict graphs that illustrate the operations of a close-intone mismatch estimator.

FIG. 14 illustrates an example of a graph depicting interleaving imagelevels in corrected IADC outputs represented for close-in tones nearf_(s)/8.

FIG. 15 illustrates an example of a graph depicting an uncorrected IADCsignal.

FIG. 16 illustrates an example of a graph depicting the IADC signalillustrated in FIG. 15 after correction has been applied.

FIG. 17 illustrates an example of a method for preventing the impact ofan interferer on mismatch profile estimation and detecting andprocessing close-in tones.

DETAILED DESCRIPTION

Systems and methods are described for determining a correlation and apower estimate for close-in tones in output of an interleavedanalog-to-digital converter (IADC). In general, for an IADC with Mnumber of ADCs (where M is an integer greater than one), there are M−1spurs. As used herein, the term “spur” denotes a spurious tone thatinterferes with the output of the interleaved ADC. Throughout thisdisclosure, these spurs are referred to as “images” of tones (orinterleaving images), since the images of the tones are correlated tothe tones in the manner described herein. As used herein, the term“close-in tones” denotes a situation where an interleaving image of asignal falls near (in terms of frequency) the signal itself.

The systems and methods described herein can address problems related tomultiple situations where near (in terms of frequency) the image of agiven tone (and/or other types of signal), an interfering tone exists.The interfering tone can be the given tone itself, which can be referredto as a close-in signal image case or a close-in tones case. In othersituations, the interfering tone can be another tone, independent fromthe given tone, which can be referred to as the independent interferercase.

For purposes of simplification of explanation, throughout thisdisclosure an example is employed where there are 4 ADCs. In thissituation, for an input tone at a frequency of f₀ and an amplitude ofA₀, an output of the interleaved ADC can have three spurs occur due tothe mismatches. In such a situation, the spurs can occur at f₀+f_(s)/4(f_(s) is the sampling frequency of the interleaved ADC), f₀+2f_(s)/4and f₀+3f_(s)/4, with respective complex amplitudes of G₁(f₀)A₀,G₂(f₀)A₀ and G₃(f₀)A₀. Based on this information, the systems andmethods described herein can estimate the three components G₁(f), G₂(f)and G₃(f) for frequencies across a band. The three components can beconverted into filter coefficients that can be employed in correctionfilters to remove the mismatches in the output of the interleaved ADC.Accordingly, the systems and methods described herein canreduce/eliminate mismatches from an interleaved ADC signal.

As noted, in certain situations, such as the close-in tone case, a tonecan fall very close/near (in terms of frequency) to an image of thetone. For example, for a tone close to f_(s)/8, f_(s)/4 or 3f_(s)/4 animage of the tone can fall very close to the tone itself. In this case,the tone and the image of the tone can be referred to as a set ofclose-in tones. The systems and methods described can determine thecorrelation and the power estimate for the set of close-in tones in thetime domain, thereby avoiding problems for processing such close-intones, such as window leakage, that would occur in the frequency domain.This correlation and the power estimate can be employed to determine themismatch profile estimate for the interleaved ADC signal for theclose-in tones.

Additionally, in situations such as the independent interferer case, awindow selection randomizer can introduce randomness into ablock-selection process of a frequency domain conversion to ensure thatthe start of each block is randomly selected so as to provide randomlyselected blocks of the interleaved ADC signal. Such randomness can avoidoccurrences of poor estimation of mismatch profile in the independentinterferer case.

FIG. 1 illustrates a block diagram of a system 2 for estimatingmismatches in an interleaved ADC 4, which in some examples can bereferred to as an ADC interleaver. The system 2 can be implemented, forexample, as a circuit, such as an integrated circuit (IC) chip. Forinstance, the system 2 could be implemented as an Application SpecificIntegrated Circuit (ASIC) chip. In some examples, portions of the system2 can be implemented as firmware accessible by a microcontroller.Additionally or alternatively, some of the blocks illustrated can beimplemented as logic implemented on a field programmable gate array(FPGA) or a combination of logic and firmware. Moreover, although eachblock of the system 2 is shown and described as performing specificfunctions, it is to be understood that in other examples, the operationsof each block can be performed by other blocks and/or in cooperationwith multiple blocks.

The interleaved ADC 4 can include an array of N number of ADCs 6 thatcan sample an analog signal (labeled in FIG. 1 as “ANALOG SIGNAL”). Theinterleaved ADC 4 can be a time-interleaved ADC. A sample clock causeseach of the N number of ADCs 6 to sample the analog signal. Thus, ateach Nth sample, a given ADC 6 samples the analog signal. Output fromeach of the N number of ADCs 6 is interleaved (e.g., multiplexed) andoutput as an interleaved ADC (“IADC”) signal, wherein N is an integergreater than one.

In FIG. 1, a clock signal 8 can be provided to a phase locked loop (PLL)10 that can provide a phase-locked clock signal to N number of frequencydividers 12. The frequency dividers 12 can each control the sampling ofa corresponding ADC 6. In the some examples, the PLL 10 can output aclock signal and each frequency divider 12 can divide the output of thePLL 10 by N. For instance, in situations where the output of the PLL 10has a frequency of 1 GHz, and there are four (4) ADCs 6, each of thefrequency dividers 12 could have an output with a frequency of 250 MHzat different phases. It is to be understood that in some examples, theclock signal 8 can be generated internally at the interleaved ADC 4 orexternal to the interleaved ADC 4 and/or the system 2. The output ofeach ADC 6 can be provided to an interleaver 13 that can multiplex(e.g., interleave) the outputs of the ADCs 6 to form an IADC signal.

Due to inherent fabrication and design tolerances, each individual ADC 6has a unique gain, sampling time offset and bandwidth and other uniquecharacteristics. Thus, a given ADC 6 has at least gain, sampling timeoffset and bandwidth mismatches relative to a reference ADC 6. The IADCsignal includes N−1 number of spurs that are a result of the mismatchesbetween the individual ADCs 6. Each set of mismatches relative to thereference ADC 6 can be referred to as a mismatch profile. The system 2can correct these mismatches. Accordingly, the IADC output by theinterleaved ADC 52 is referred to as an uncorrected IADC signal (labeledin FIG. 1 as “IADC (UNCORRECTED)”.

The uncorrected IADC signal can be provided to a window selectionrandomizer 14. The window selection randomizer 14 can provide blocks ofsamples (e.g., of some fixed length S, such as 512 samples) from theuncorrected IADC output to the frequency domain processor 16. The windowselection randomizer 14 can introduce randomness into theblock-selection process. In particular, the window selection randomizer14 can ensure that the start of each block is randomly selected so as toprovide randomly selected blocks of the IADC signal.

The frequency domain processor 16 can store and process the randomlyselected blocks of samples of the IADC signal. The frequency domainprocessor 16 can be configured to apply a windowing function and a FastFourier Transform (FFT) function on the randomly selected blocks. Thewindowing function can be implemented, for example, as theBlackman-Harris windowing function. The frequency domain processor 16can provide frequency domain data that characterizes the FFT of thewindowed blocks of the uncorrected IADC signal to a mismatch profileestimator 18. The FFT of a selected block can be referred to as an FFTblock that characterizes the spectral content of the uncorrected IADCsignal as a function of contiguous frequency bands referred to as FFTbins. Multiple such FFT blocks characterize the time variation of thespectral content of the uncorrected IADC signal

The mismatch profile estimator 18 can apply a validity check to each ofthe FFT bins within an FFT block and/or across multiple FFT blocks. Inparticular, the validity check can perform a first validity check thatcompares a power of a given FFT bin to a first threshold, and rejectsFFT bins that have a power below the first threshold. In this manner,the first validity check can reject low power signals and/or mismatchesthemselves from being processed as valid inputs for estimating themismatch profile, thereby avoiding possible interferer generated bias.Additionally, the mismatch profile estimator 18 can perform a secondvalidity check that compares a ratio of a power of a signal bin and apower of an image bin (signal-to-image power ratio) to a secondthreshold. An image bin is an FFT bin that corresponds to the locationof the image of the signal, and the signal bin is an FFT bin thatcorresponds to the location of the signal. If the signal-to-image powerratio is below the second threshold, the corresponding image bin can berejected. The mismatch profile estimator 18 can determine and accumulatea correlation, signal and image power, and noise variance noise varianceestimate for all the non-rejected FFT bins over multiple FFT blocks.

The mismatch profile estimator 18 can calculate an instantaneousfrequency domain mismatch profile estimate for each input frequency. Themismatch profile estimator 18 can also calculate an uncertainty of eachinstantaneous frequency domain mismatch profile estimate based on theaggregated statistics (e.g., correlation, signal and image power andnoise variance estimate). Data characterizing the instantaneousfrequency domain estimate and the corresponding uncertainty can beemployed by the mismatch profile estimator 18 to interpolate thefrequency domain mismatch profile estimate for each the ADCs 6 over arange of frequencies, including band edges. In particular, the mismatchprofile estimator 18 can provide a frequency domain mismatch profile foreach of the ADCs 6 in the interleaved ADC 4.

The mismatch profile estimator 18 can provide the frequency domainprofiles of each filter to a close-in tone analyzer 24. Moreover, theclose-in tone analyzer 24 can receive FFT bin information, such as thecomplex amplitude at each of the FFT bins, or some subset thereof,across multiple FFT blocks (e.g., the same bin number in multiple FFTblocks) from the frequency domain processor 16. The close-in toneanalyzer 24 can also receive the uncorrected IADC signal from theinterleaved ADC 4. The close-in tone analyzer 24 can process tones thathave images too closely positioned by frequency to be distinguishablethrough FFT analysis, which tones can be referred to as close-in tones.The close-in tone analyzer 24 can estimate a power of the frequencydomain profile at close-in tone bins to determine if the power is abovea given threshold. Additionally, the close-in tone analyzer 24 cananalyze an uncertainty of the frequency domain profiles that can beprovided from the mismatch profile estimator 18 to determine theuncertainty is above another threshold. In response to determining thatthe estimated power of the frequency domain profile is above the giventhreshold and/or that uncertainty is above the other threshold, theclose-in tone analyzer 24 can implement a close-in tone estimationprocess on the set of close-in tones.

The close-in tone estimation process can employ a time domain algorithmto estimate a correlation signal for the given tone with the image ofthe given tone and a power estimate for the given tone. The correlationsignal and the power estimate for the given tone can be provided to themismatch profile estimator 18. The mismatch profile estimator 18 canemploy the correlation signal and the power estimate for the given toneto estimate the frequency domain mismatch profile in the mannerdescribed.

The mismatch profile estimator 18 can provide the frequency domainmismatch profiles (including those determined for close-in tones) ofeach of the ADCs 6 to a time domain converter 20. The time domainconverter 20 can employ an Inverse Fast Fourier Transform (IFFT) toconvert the mismatch profile of each of the ADCs 6 into filtercoefficients in the time domain. The filter coefficients can be providedto a time domain corrector 22. The time domain corrector 22 can employthe filter coefficients in correction filters to subtract the mismatchprofile for each of the ADCs 6 from the uncorrected IADC signal toproduce a corrected IADC output.

FIG. 2 illustrates another block diagram of a system 50 for estimatingmismatches in an interleaved ADC 52. The system 50 can be employed forexample, to implement the system 2 illustrated in FIG. 1. Theinterleaved ADC 52 can include M number of parallel ADCs 54 that eachsample an analog signal (labeled in FIG. 2 as “ANALOG SIGNAL”), where Mis an integer greater than one. For purposes of simplification ofexplanation, in a simplified given example, (hereinafter, “the givenexample”) is presumed that there are 4 ADCs 54 in interleaved ADC 52,but in other examples more or less ADCs 54 can be employed. The outputfrom each of the 4 ADCs 54 can be multiplexed (e.g., interleaved) by aninterleaver 55 and output as an uncorrected IADC signal (labeled in FIG.2 as IADC (UNCORRECTED)). The mismatch between ADCs 54 can be due, forexample, to fabrication and design tolerances, such that each individualADC 54 has a unique gain, sampling time offset and bandwidth and/orother unique characteristics. As used herein, each mismatch representsan aggregate mismatch (or simply a “mismatch”) due to each of ADC's 54individual, gain, sampling tine, bandwidth and/or other characteristics.

FIG. 3 illustrates an example a graph 100 of an uncorrected IADC outputrepresented in the given example. In the graph 100, amplitude of asignal, in decibels relative to full scale (dBFS) are plotted as afunction of a frequency, f, in Megahertz (MHz). As illustrated in thegraph 100, in the given example, there are 3 images of the given inputtone at the frequencies, f₀+f_(s)/4, f₀+2f_(s)/4 and f₀+3*f_(s)/4 withrespective complex amplitudes G₁(f₀)*A₀, G₂(f₀)*A₀ and G₃(f₀)*A₀ for theinput tone of amplitude A₀. Referring back to FIG. 2, Equation 1characterizes the uncorrected IADC output in the frequency domain,whereby Y(f) can be derived.

$\begin{matrix}{{Y(f)} = {{{X(f)}{\mathbb{e}}^{{- {j2\pi}}\; f\;\Delta}} + {\sum\limits_{{k\; 1} = 0}^{3}{{X\left( {f - \frac{k\; 1\; f_{s}}{4}} \right)}{G_{k\; 1}\left( {f - \frac{k\; 1f_{s}}{4}} \right)}}}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

The uncorrected IADC signal can be provided to a window selectionrandomizer 56. Conceptually, the window selection randomizer can beimplemented as a control of a switch 58 that couples the uncorrectedIADC output to a frequency domain processor 60. The window selectionrandomizer 56 can be configured to provide blocks of samples (of somefixed length S, such as 512 samples) of the uncorrected IADC signal tothe frequency domain processor 16. The window selection randomizer 14can introduce randomness into the block-selection process. Specifically,the window selection randomizer 14 can ensure that the start of eachblock is randomly selected so as to provide randomly selected blocks ofthe IADC signal. In particular, the starting point of each such blockcan be selected randomly, such that the window selection randomizer 56can provide randomly selected blocks.

For instance, in a simplified example, exactly one block of S number ofsamples (e.g., 512 samples) needs to be selected for every L samples ofthe uncorrected IADC output, wherein L is a multiple of M thatcorresponds to a number of the ADCs 54. In this situation, the startingsample for the ith block is selected to be at (i−1)*L+τ, where τ is arandom number with value from the set of {0, M, 2*M, . . . , (L/M−1)*M}with equal probabilities. Such a randomized block selection canfacilitate reduction of the impact of a second signal (an interferer)near one of the images of a first signal on the estimation of mismatchprofile at the frequency of the first signal.

The frequency domain processor 56 can store and process the randomlyselected blocks. Additionally, certain blocks that violate certainconditions, such as blocks close to saturation and/or blocks with anoverall power less than a threshold can be rejected by the frequencydomain processor 60. In some examples, the frequency domain processor 60can be configured to apply a windowing function and an FFT function tothe non-rejected randomly selected blocks of the uncorrected IADCsignal. It is noted that in some examples, the windowing function andthe FFT function can be applied to all of the randomly selected blocksand the rejection of the blocks can be performed after the FFT of therandomly selected blocks is determined. The windowing size can beselected to ensure that window leakage at a frequency sufficientlyremoved from the signal (e.g., a tone) is about −100 dBc, therebyensuring that the error in the estimate of the frequency domain mismatchprofile, G_(k)(f) is less than about −80dBc. In one example, thewindowing function can be implemented, for example, as theBlackman-Harris windowing function with a window length of about 512samples. In other examples, different window sizes can be employed.

The windowing function can cause interference due to an independentsignal in an image band. FIG. 4 illustrates this concept. In particular,FIG. 4 depicts a graph 200 plots an amplitude of a two-tone example(hereinafter, “the two-tone example) with a first tone A₁ and a secondtone, A₂ as a function of frequency (bin index). In the two-toneexample, the window leakage (e.g., window attenuation) due to thewindowing function, W(ƒ) can introduce an error in the calculation ofthe signal-image correlation. For each block of data, the errorcorresponds to a complex tone with a frequency of δf at a block startinstant. Stated differently, as illustrated in the graph 200, in thetwo-tone example, leakage at the second tone, A₂W(δƒ) on the location ofthe image of the first tone, G₁A₁, thereby introducing correlationerrors. For instance, in the two tone example, the error in thecorrelation (without randomization of block selection), Er^(i) for FFTblock number i can be calculated with Equation 2.

$\begin{matrix}{{\sum\limits_{i}{Er}^{i}} = {A_{1}A_{2}{W\left( {\delta\; f} \right)}{\sum\limits_{i}{\mathbb{e}}^{{- {j2}}\;\pi\;{iL}\;\delta\; f}}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

wherein:

$j = \sqrt{- 1}$(throughout this disclosure);

${{\delta\; f} = \frac{i}{L\; T_{s}}};$

L is the period of block selection specified in number of samples of theuncorrected IADC signals; and

$T_{s} = {\frac{1}{f_{s}}.}$

From Equation 2, in situations where blocks are selected every LT_(s)seconds, correlation errors for

${\delta\; f} = \frac{i}{{LT}_{s}}$(i is a positive integer), will be in phase and add up upon aggregation,which can introduce bias of estimates for G_(k)(f). Referring back toFIG. 2, as noted, the window selection randomizer 56 provides randomlyselected blocks to the frequency domain processor 60 based on a randomnumber, τ. FIG. 5 illustrates a conceptual example of a randomized blockselection 300. In FIG. 5, the frequency domain processor 60 selectsblocks at time periods of L. As is illustrated in FIG. 5, the windowselection randomizer 56 can randomly select a starting point for eachblock based on the random number, τ, wherein τ is a random number withvalue from the set of {0, M, 2*M, . . . , (L/M−1)*M} with equalprobabilities. Moreover, some of the randomly selected blocks may beoverlapping. However, such overlapping blocks of data do not introducebiases for the estimations of G_(k)(f).

Referring back to FIG. 2, such a randomized delay can ensure that theerror term, the complex tone at δf, is uniformly sampled about a unitcircle for of δf=i/LT_(s). In this manner, correlation errors introducedby the interferer for every block of data are not in-phase (e.g., forδf>0). Accordingly, the interferer appears “noise-like” (e.g., a mean of‘0’) after aggregation.

FIG. 6 illustrates a block diagram of an example of a random numbergenerator 350 that can provide τ to the window selection randomizer 56illustrated in FIG. 2. The random number generator 350 can include alinear feedback shift register (LFSR) based K-bit random numbergenerator 352. The value of K is selected such that, 2^(K) is muchgreater than L/M. That is, 2^(K)>>L/M. The LFSR based K-bit randomnumber generator 352 can output a random number r that can be mixed withan arbitrary value of V. The mixed output can be processed by a leastsignificant bit (LSB) dropper 354. The LSB dropper 354 can divide themixed output function by 2^(K) to remove K number of the LSBs andprovide an output of K/2^(K) that can be multiplied by M to generate τthat can be employed as the random number explained with respect toFIGS. 2 and 8. The random number generator 350 can be employed to ensurethat the output of τ is distributed substantially uniformly about theset of {0, M, 2*M, . . . , (L/M−1)*M}. It is to be understood that inother examples, other methods could be employed for generating therandom number.

Referring back to FIG. 2, the frequency domain processor 60 can providefrequency domain data that characterizes the FFT of the selected blocksof the uncorrected IADC signal to a mismatch profile estimator 62. Themismatch profile estimator 62 can be employed to implement the mismatchprofile estimator 18 of FIG. 1. The mismatch profile estimator 62 candetermine a correlation between tones, C_(k)(f) for each of the FFTbins. The correlation between two tones, C_(k)(f) can be characterizedby Equation 3.

$\begin{matrix}{{C_{k}(f)} = {{{G_{k}(f)}{{Y(f)}}^{2}} + {{G_{4 - k}^{*}\left( {f + \frac{k\; f_{s}}{4}} \right)}{{Y\left( {f + \frac{k\; f_{s}}{4}} \right)}}^{2}} + {n^{\prime}(f)}}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

In the given example, by employing Equation 3, the mismatch profileestimator 62 can correlate the conjugate of the given input tone (A₀*)with the appropriate image (G_(k)A₀) to derive Equation 4.C _(k)(f ₀)=G _(k)(f ₀)|A ₀|²  Equation 4

The mismatch profile estimator 62 can measure C_(k)(f₀) at the FFT bins.Additionally, the mismatch profile estimator 62 can estimate a power, indecibels to full scale (dBFS) for each FFT bin and perform a firstvalidity check to determine if the power of each tone is above athreshold. The mismatch profile estimator 62 can also perform a secondvalidity check to determine if a signal-to-image power ratio (e.g., aratio of signal power to image power) is greater than a threshold (e.g.,second threshold) to limit estimation errors due to interferer generatedbias. Tones that fail the first or second validity checks can berejected.

The non-rejected tones, namely tones that passed the first and secondvalidity checks are aggregated, as well as correlations, signal andimage power and noise variance estimates are accumulated for theselected FFT bins across multiple FFT blocks. The mismatch profileestimator 62 can aggregate correlation values (when the values pass thefirst and second validity checks) for a predetermined (e.g.,preprogrammed) number of the FFT blocks.

The sum of correlation and the sum of signal and image power for theselected blocks can be stored by the mismatch profile estimator 62 asaggregated statistics, for example in a non-transitory machine readablemedium (e.g., a memory). In some examples, the aggregated statistics canbe stored as a data structure (e.g., a linked list). Moreover, themismatch profile estimator 62 can estimate unknown mismatch profiles,G_(k) (m) for the non-rejected (valid) tones. The mismatch profileestimator 62 can also determine an aggregate power of both contributors(a tone, and an image of the tone).

The aggregate power of both contributors can be stored by the mismatchprofile estimator 62 in the aggregate statistics. Furthermore, themismatch profile estimator 62 can determine an aggregate noise presentin the FFT bins. The mismatch profile estimator 62 can determine anaggregate noise presence based on the aggregate noise in each of the FFTbins. Moreover, the mismatch profile estimator 62 can determine a noisevariance, R^(k)(m) based on the aggregated noise. The noise variance,R^(k)(m) can also be stored in the aggregated statistics by the mismatchprofile estimator 62.

The mismatch profile estimator 62 can employ the correlation valuesstored in the aggregate statistics to calculate (e.g., estimate) aninstantaneous frequency domain mismatch profile estimate, G_(k)(f₀) foreach input signal. In the given example, since C_(k)(f₀) and |A₀|² isknown (via the aggregated statistics), G_(k)(f₀) (including G₁(f₀),G₂(f₀) and G₃(f₀)) can be determined/estimated.

Data characterizing the instantaneous frequency domain mismatch profileestimate, G_(k)(f) can be processed by an averaging filter 64 of themismatch profile estimator 62. The averaging filter 64 can include, forexample, a Kalman filter, an infinite input response (IIR) filter or thelike. The averaging filter 64 can store historical data characteringpast instantaneous frequency domain mismatch profile estimates, G_(k)(m)for different frequencies. The averaging filter 64 can determine anestimate of the frequency domain mismatch profile G_(k)(m), recursively.

The estimate of the frequency domain mismatch profile, G_(k)(m) can beprovided from the averaging filter 64 to a time domain converter 66. Thetime domain converter 66 can modify an estimate for G_(k)(m) at the0^(th) bin and a last bin, namely a bin at f_(s)/2 (e.g., 128^(th) binfor 256-point FFT) to reflect the fact that h_(i) (a correction filter,as explained herein) is a real filter. Once h_(i) is a real filter,G₂(0) and G₂(128) are real, G₃(0)=G₁*(0) and G₃(128)=G₁*(128). Theseconditions can be imposed on the G_(k)(m) estimates. The remaining tonescan be linearly interpolated and extrapolated to generate an estimate ofG_(k)(m) for frequencies across a band of interest to generate anestimate for a continuous frequency domain mismatch profile, G_(k)(f).Additionally, in some examples, smoothing can be implemented withshaping filters for regions outside the band of interest topredetermined boundary conditions. The prior G_(k)(f) estimates (e.g.,from the averaging filter 64) can be provided to a close-in tone control68 of a close-in tone analyzer 71. Additionally, the frequency domainprocessor 60 can provide the FFT bins to the close-in tone control 68.The close-in tone control 68 can analyze the aggregated statistics toidentify an FFT output corresponding to a close-in tone bin. Theclose-in tone control 68 can also monitor the prior G_(k) (f) estimatesto detect prior G_(k)(f) estimates that are near close-in tones.

FIG. 7 illustrates a graph 400 that illustrates close-in tones. Thegraph 400 plots an amplitude of a signal (in dB) as a function offrequency. A tone labeled ‘A₀’ has a correlated image labeled A₀*G₃*. Inthe graph 400, a dashed line 402 represents the window leakage due tothe windowing function W(ƒ). As is illustrated, the correlated imageA₀*G₃* falls “too close” (in frequency) to the tone A₀ to distinguishthe correlated image A₀*G₃* from the tone A₀ using FFT analysis due tothe window leakage indicated by the dashed line 402. Thus, these tonescan be referred to as “close-in tones”. It is noted that in the graph400 the tone A₀ is close to f_(s)/8.

Referring back to FIG. 2, for an input tone close to kf_(s)/2M,(including f_(s)/8, f_(s)/4 and 3f_(s)/8, when there are 4 ADCs 54, suchthat M is equal to 4) an image of the of the input tone (an image band)can fall close to the input tone, thereby forming a set of close-intones, where k is an integer selected from the set of {1, 2, . . . ,M−1}. The close-in tone control 68 can include a trigger control 70 thatcan provide a close-in trigger to a close-in tone mismatch estimator 72of the close-in tone analyzer 71. The close-in tone control 68 can parsethe FFT bins to identify each close-in tone bin (an FFT bincorresponding to close-in tone inputs) and provide FFT data at eachclose-in tone bin to the trigger control. Additionally, the close-intone control 68 can parse the prior estimates of the mismatch profiles,G_(k)(f) to identify each prior G_(k)(f) estimate that is near close-intones. As used herein, the prior G_(k)(f) estimates that are “nearclose-in tones” can be the prior G_(k)(f) estimates in a set of FFT binsadjacent to the close-in tones.

FIG. 8 illustrates a block diagram of an example of a trigger control450 that could be employed to implement the trigger control 70 of FIG.2. The trigger control 450 can include a power estimator 452 that candetermine a power (P) of each detected close-in tone bin. Additionally,the trigger control 450 can include a power thresholder 454 that candetermine if the power of a given close-in tone bin is greater than apower threshold. Conceptually, the power thresholder 454 can determinewhether the close-in tone bin includes a real set of close-in tones, andnot simply noise. If the power of the given close-in tone bin is greaterthan the power threshold, the power thresholder 454 can provide an ‘ON’signal (e.g., a logic ‘1’) to an AND gate 456 of the trigger control450. In contrast, if the power of the given close-in tone bin is lessthan the power threshold, the power thresholder 454 can provide an ‘OFF’signal (e.g., a logic ‘0’) to the AND gate 456 of the trigger control450.

Additionally, the trigger control 450 can include an uncertaintythresholder 458 that can determine if an uncertainty of prior G_(k)(f)estimates near close-in tones is greater than an uncertainty threshold.The uncertainty threshold can indicate whether the uncertainty of theprior G_(k)(f) is small enough to employ as the profile mismatchestimate for the close-in tone set, such that a new profile mismatchestimate need not be calculated. If the uncertainty of the priorG_(k)(f) estimates are greater than the uncertainty threshold (e.g.,uncertainty too large), the uncertainty thresholder 458 can provide an“ON” (e.g., logic ‘1’) signal to the AND gate 456. Conversely, if theuncertainty of the prior G_(k)(f) estimates are less than theuncertainty threshold (e.g., uncertainty sufficiently small), theuncertainty thresholder 458 can provide an “OFF” (e.g., logic ‘0’)signal to the AND gate 456. The output of the AND gate 456 cancorrespond to a close-in trigger that can be provided to the close-intone mismatch estimator 72 illustrated in FIG. 2.

The close-in tone mismatch estimator 72 can receive the uncorrected IADCsignal. The close-in tone mismatch estimator 72 can be configured toestimate data that can be employed to estimate mismatches that occuraround close-in tones in response to receiving a close-in trigger fromthe trigger control 70. Such data can include a correlation and a powerestimate for the close-in tones. Specifically, the close-in tonemismatch estimator 72 can provide a close-in correlation estimate,z_(i)(n) and a power estimate, z₂(n) can be calculated by the close-intone mismatch estimator 72 in response to a trigger signal. Theoperations of the close-in tone mismatch estimator 72 can be completedin the time domain, thereby obviating the problems associated with FFTanalysis (e.g., window leakage) of close-in tones.

FIG. 9 illustrates a block diagram of a close-in tone mismatch estimator500 that could be employed to implement the close-in tone mismatchestimator 72 of FIG. 2. The close-in tone mismatch estimator 500 canreceive the close-in trigger (e.g., provided by the trigger control 450)and the uncorrected IADC signal (labeled in FIG. 9 as “IADC(UNCORRECTED)”. An uncorrected IADC signal can be represented as y(n).The close-in tone mismatch estimator 500 can include a mixer 502 thatcan mix the ideal IADC signal with a complex exponential sequence 504.In the example illustrated in FIG. 9, the complex exponential sequence504 is e^(−|2πfs/8nTs), which corresponds to a frequency shift off_(s)/8 of the uncorrected IADC signal. However, in other examples, suchas a close-in tone being detected at f_(s)/4 or 3f_(s)/8, a differentcomplex exponential sequence 504 could be employed.

The output of the mixer 502 can be provided to a downsampler 506. Thedownsampler 506 can apply anti-alias filtering and then reduce thesampling rate of the signal output by the mixer 502, which process canalso be referred to as decimation. In some examples, the sampling ratecan be reduced by about 1/32. Thus, for an uncorrected IADC signal witha sampling rate of about 1 GHz, the downsampler 506 can output a signalwith a downsampled rate of about 32 MHz. The output of the downsampler506, y_(d)(n) which corresponds to a frequency shifted, downsampledsignal, can be provided to a squarer 508 and a power estimator 510. Thesquarer 508 can calculate a square of y_(d)(n) in the time domain(denoted in FIG. 9 as “(.)²”), d₁(n). The power estimator 510 cancalculate a magnitude of the square (denoted in FIG. 9 as “|(.)|²” ofy_(d)(n), which can correspond to an approximate power, d₂(n). Theoutput of the squarer 508 and the power estimator 510 can be provided tolow pass filters (LPFs) 512 and 514. The LPFs 512 and 514 can have acutoff frequency sufficient to remove unwanted higher frequency terms.As illustrated in FIG. 9, the output of the LPF 512 can be a correlationestimate, z₁(n)=2G₃|A|², for a tone ‘A’. Moreover, as illustrated inFIG. 9, the output of the LPF 514 can be a power estimate, z₂(n)≈|A|²for the tone ‘A’.

FIGS. 10-13 depict graphs 550, 560, 570 and 580 that illustrate theoperations of the close-in tone mismatch estimator 500. The graphs 550,560, 570 and 580 plot an amplitude (in dB) of a signal as a function offrequency. Moreover, the graphs 550, 560, 570 and 580 employ the sameidentifiers to denote the same signals and variables. In the exampleillustrated in FIGS. 10-13, an input tone ‘A’ is near f_(s)/8 and thusforms a set of close in tones with an image with a complex amplitude of‘A*G₃’ In particular, in the graph 550, illustrates an example of aspectrum of y(n) (e.g., input into the mixer 502). In the graph 550, theinput tone ‘A’ and the image ‘A*G₃’ are each separated from f_(s)/8 byan equal (or nearly equal) amount, δf. In the graph 560, the spectrum ofy_(d)(n) (output by the downsampler 506) is plotted. As is illustrated,the spectrum has been frequency shifted (relative to y(n)) such that theinput tone ‘A’ and the image ‘A*G₃’ are separated from the origin (‘0’)by δf.

The graph 570 depicts a spectrum of d₁(n) (the output of the squarer508). As is illustrated, in the graph 570, a DC signal (frequency of‘0’) with a magnitude of ‘2G₃|A|²’ can be calculated by the squarer 508.Similarly, graph 580 depicts a spectrum of d₂ (n) (the output of thepower estimator 510). As is illustrated in the graph 580, a DC signalwith a magnitude of |A|²(1+|G₃|²) (which is approximately equal to |A|²)can be calculated. It is noted that the non-DC signals of graphs 570 and580 can be removed by the LPFs 512 and 514, respectively to calculatez₁(n) and z₂(n).

Referring back to FIG. 2, the mismatch profile estimate for G₃ can becalculated using simple algebra from the outputs z₁(n) and z₂(n). Thus,the outputs for the correlation estimate, z₁(n) and the power estimatez₁(n) of the close-in tones can be provided to the averaging filter 64such that G_(k)(f) can be derived and tracked for the close-in tones ofthe uncorrected IADC signal.

The time domain converter 66 can employ an IFFT to the convertcontinuous frequency domain mismatch profile, G_(k)(f) into a complexdiscrete time domain filter function, g_(k)(m). Each of the complexfilter functions g_(k)(m) may correspond to complex filters (e.g.,filters with coefficients that may or may not be complex numbers).

The time domain converter 66 can convert the time domain filterfunctions g_(k)(m) into filter coefficients h_(i)(m) by employingEquation 5. Each of the filter coefficients, h_(i)(m) can correspond toreal filters (e.g., filters that have real number coefficients). Asnoted, since h₀(m)=0, indicating that there is no correction applied tothe output of the reference ADC 54, and thus, h₀(m) does not need to beimplemented. Accordingly, there are less filter coefficients h_(i) (m)that are implemented than the number of g_(k)(m) filters functions.

$\begin{matrix}{{{h_{i}(m)} = {\sum\limits_{k = 0}^{M - 1}{{g_{k}(m)}{\mathbb{e}}^{\frac{{j2\pi}\;{ik}}{M}}}}},} & {{Equation}\mspace{14mu} 5}\end{matrix}$for all m

Wherein:

i runs from 1 to M−1;

h₀(m)=0.

The filter coefficients, h_(i)(m) can be provided to time domaincorrector 74 that can receive the uncorrected IADC signal from theinterleaved ADC 52. The time domain corrector 74 can employ the filtercoefficients, h_(i)(m) in correction filters to remove the spurs causedby the interleaving of the M number of ADCs 54 and output a correctedIADC output (labeled in FIG. 2 as “IADC (CORRECTED)”).

By employing the system 50, an estimation of a mismatch profile betweenthe M number of ADCs 54 can be achieved. Additionally, the mismatchprofile between the M number of ADCs 54 can be estimated in situationswhere a tone is close-in (in terms of frequency) with an image of thetone.

FIG. 14 illustrates an example of a graph 600 depicting a corrected IADCoutputs represented for close-in signals near f_(s)/8. The graph 600plots a magnitude (in dB) of an interleaving-image to signal ratio as afunction of frequency (in MHz) before and after the correction of theIADC signal described with respect to FIGS. 1 and 2. As is illustratedin the graph 600, the interleaving image to signal ratio has improved byat least about −45 dB.

FIG. 15 illustrates an example of a graph 650 depicting an uncorrectedIADC signal represented. FIG. 16 illustrates an example of a graph 670depicting the IADC signal illustrated in FIG. 15 after correction hasbeen applied. In the graphs 650 and 670 amplitude of a signal, in dBc isplotted as a function of an input frequency in MHz. In the graph 650 anindependent tone is input close to an image of a wideband signal,thereby providing a strong interference to mismatch estimation over thefrequencies occupied by the wideband signal. As illustrated in the graph670 at block 654, the impact of the interfering signal is reduced due tothe introduction of the randomly selected blocks.

In view of the foregoing structural and functional features describedabove, an example method will be better appreciated with reference toFIG. 17. While, for purposes of simplicity of explanation, the examplemethod of FIG. 17 is shown and described as executing serially, it is tobe understood and appreciated that the present examples are not limitedby the illustrated order, as some actions could in other examples occurin different orders, multiple times and/or concurrently from that shownand described herein. Moreover, it is not necessary that all describedactions be performed to implement a method. The example method of FIG.17 can be implemented as instructions stored in an IC chip (e.g., asfirmware) that are executable by a processor (e.g., a microcontroller)and/or as logic (e.g., an FPGA).

FIG. 17 illustrates an example of a method 700 for preventing an impactof independent interferers on mismatch profile estimation. Additionallyor alternatively, the method 700 can be employed for detecting andprocessing close-in tones. It is noted that in some examples, the methodof preventing the impact of independent interferers in mismatch profileestimation and the method of method of detecting and processing close-intones can be employed independently. However, in the method 700, theactions for the preventing the impact of interferers on the mismatchprofile estimation, and the detecting and processing the close-in tonesare described in combination. The method 700 could be implemented, forexample by the system 2 of FIG. 1 and/or the system 50 of FIG. 2. At710, a window selection randomizer (e.g., the window selectionrandomizer 14 of FIG. 1) can randomize a block selection to providerandomly selected blocks of input samples of the IADC signal. At 720, afrequency domain processor (e.g., the frequency domain processor 16 ofFIG. 1) can store and process the randomly selected blocks of inputsamples. At 730, the frequency domain processor can apply a windowingfunction to the randomly selected blocks of input samples. At 740, thefrequency domain processor can apply an FFT to convert the windowed andrandomly selected blocks into the frequency domain.

At 745, a mismatch profile estimator (e.g., (e.g., the mismatch profileestimator 18 of FIG. 1) can aggregate statistics for all (or a subset)of the FFT bins over multiple FFT blocks to generate aggregatedstatistics. At 750, the mismatch profile estimator can estimate aninstantaneous frequency domain mismatch profile, G_(k)(m) based on theaggregated statistics. At 760, the mismatch profile estimator canaverage the frequency domain mismatch profile, G_(k)(m) over time.Moreover, in some situations, the averaging over time can be performedacross multiple FFT blocks.

At 770, a close-in tone analyzer (e.g., the close-in tone analyzer 24 ofFIG. 1) can detect set of close-in tones, wherein a tone falls close to(in terms of frequency) an image of the tone. At 780, the close-in toneanalyzer can employ time domain analysis to estimate the correlation andthe power of the close-in tones. The estimate for the correlation andthe power of the close-in tones can be provided back to the mismatchprofile estimator.

At 790, a time domain converter (e.g., the time domain converter 20 ofFIG. 1) can convert the frequency domain mismatch profile, G_(k)(m) tothe time domain to form a time domain mismatch profile, g_(k)(m). At800, the time domain converter can determine filter coefficients,h_(i)(m) based on the time domain mismatch profile, g_(k)(m). The filtercoefficients can be employed to correct the IADC signal.

What have been described above are examples. It is, of course, notpossible to describe every conceivable combination of components ormethodologies, but one of ordinary skill in the art will recognize thatmany further combinations and permutations are possible. Accordingly,the disclosure is intended to embrace all such alterations,modifications, and variations that fall within the scope of thisapplication, including the appended claims. As used herein, the term“includes” means includes but not limited to, the term “including” meansincluding but not limited to. The term “based on” means based at leastin part on. Additionally, where the disclosure or claims recite “a,”“an,” “a first,” or “another” element, or the equivalent thereof, itshould be interpreted to include one or more than one such element,neither requiring nor excluding two or more such elements.

What is claimed is:
 1. A system comprising: a close-in tone controlconfigured to: detect a set of close-in tones of an interleaved analogto digital converter (IADC) signal; and output a trigger signal inresponse to the detection; and a close-in tone mismatch estimatordetermines a correlation and a power estimate for the set of close-intones in the IADC signal in response to the trigger signal.
 2. Thesystem of claim 1, wherein the set of close-in tones comprises: a tonewith a frequency near a particular fraction of the sampling frequency(f_(s)) of the IADC signal; and an image of the tone with a frequencynear the frequency of the tone.
 3. The system of claim 2, wherein thetone has a frequency near any frequency defined by kf_(s)/2M, wherein kis a positive integer less than M, and M defines a number of componentanalog-to-digital converters (ADCs) in an interleaved ADC that providesthe IADC signal.
 4. The system of claim 2, wherein the close-in tonemismatch estimator comprises a mixer to mix the IADC signal with afrequency shift word to generate a frequency shifted signal.
 5. Thesystem of claim 4, wherein the close-in tone mismatch estimator furthercomprises a downsampler to reduce the sampling frequency of the IADCsignal.
 6. The system of claim 5, wherein the close-in tone mismatchestimator further comprises a squarer that determines a square of theIADC signal for the close-in tones in the time domain.
 7. The system ofclaim 5, wherein the close-in tone mismatch estimator further comprisesa power estimator that determines a power estimate of the close-in tonesin the time domain.
 8. The system of claim 7, wherein an output of thesquarer is provided to a low pass filter that removes high frequencysignals.
 9. The system of claim 1, further comprising: an interleavedanalog-to-digital converter (ADC) comprising component ADCs, theinterleaved ADC outputs the IADC signal, wherein the IADC signalcomprises spurious signals generated from mismatches in the componentADCs.
 10. The system of claim 1, further comprising a window selectionrandomizer that randomizes selection of blocks of the IADC signal basedon a random number.
 11. The system of claim 10, wherein the randomnumbers are substantially uniformly distributed over a predetermined setof numbers.
 12. The system of claim 10, further comprising a frequencydomain processor data selector configured to: receive the randomlyselected blocks of the IADC signal; apply a windowing function to therandomly selected blocks of the IADC signal to provide windowed blocksof data; and convert the windowed blocks of data into the frequencydomain to provide a frequency domain representation of the IADC signal.13. The system of claim 1 further comprising a profile mismatchestimator determines an estimate of a frequency domain mismatch profilebased in part on the correlation and the power estimate for the set ofclose-in tones in the IADC.
 14. The system of claim 1, wherein theclose-in tone control receives data from a mismatch profile estimatorcharacterizing an estimate of a mismatch profile for tones near infrequency to the set of close-in tones, wherein the trigger signal isprevented from being output in response to determining that the estimateof the mismatch profile for the tones near in frequency to the set ofclose-in tones has an uncertainty below an uncertainty threshold. 15.The system of claim 1, wherein the close-in tone control prevents thetrigger signal from being output in response to determining a FastFourier Transform (FFT) bin corresponding to the set of close-in toneshas a power below a power threshold.
 16. An integrated circuit (IC) chipcomprising: an analog-to-digital converter (ADC) interleaver comprisinga plurality of ADCs that are each configured to sample an analog signalin response to a clock pulse, wherein the Interleaved ADC outputs aninterleaved ADC (IADC) signal that comprises a plurality of spurs formedfrom mismatches between the plurality of ADCs; a frequency domainprocessor determines a frequency domain representation of theinterleaved IADC signal; a close-in tone control configured to: detect aset of close-in tones of the IADC signal based on the frequency domainrepresentation of the IADC signal; receive data from a mismatch profileestimator characterizing an estimate of a mismatch profile for a tonenear in frequency the set of close-in tones; and output a trigger signalin response to detecting that a Fast Fourier Transform (FFT) bincorresponding to the set of close-in tones has a power above a powerthreshold and in response to determining that the estimate of themismatch profile for the tones near in frequency the set of close-intones has an uncertainty above an uncertainty threshold; and a close-intone mismatch estimator determines a correlation and a power estimatefor the set of close-in tones in the IADC signal in response to thetrigger signal.
 17. The IC chip of claim 16, wherein the close-in tonemismatch estimator determines a square of the IADC signal for the set ofclose-in tones and a power estimate for the set of close-in tones. 18.The IC chip of claim 16, further comprising a window selectionrandomizer that randomizes selection of blocks of the IADC signal.
 19. Amethod comprising: randomizing selection of blocks of samples aninterleaved analog-to-digital (IADC) signal to provide randomly selectedblocks; applying a windowing function to the randomly selected blocks ofsamples of the IADC signal; applying a Fast Fourier Transform (FFT) tothe selected blocks of samples to determine a frequency domainrepresentation of the IADC signal; and estimating a frequency domainmismatch for the interleaved ADC signal.
 20. The method of claim 19,further comprising determining a correlation and a power estimate of aset of close-in tones of the interleaved ADC signal.